1. **State the problem:** Yaritza has a deck measuring 7 feet by 20 feet. She wants to increase each dimension by the same length $x$ so that the new area is triple the original area. 2. **Write the formula for area:** The area of a rectangle is given by $$A = \ell \times w$$ where $\ell$ is length and $w$ is width. 3. **Original area:** $$A_{original} = 20 \times 7 = 140$$ 4. **New area:** The new dimensions are $(20 + x)$ and $(7 + x)$, so the new area is $$A_{new} = (20 + x)(7 + x)$$ 5. **Set up the equation:** The new area should be triple the original area, so $$ (20 + x)(7 + x) = 3 \times 140 = 420 $$ 6. **Expand the left side:** $$ (20 + x)(7 + x) = 20 \times 7 + 20x + 7x + x^2 = 140 + 27x + x^2 $$ 7. **Form the quadratic equation:** $$ 140 + 27x + x^2 = 420 $$ 8. **Bring all terms to one side:** $$ x^2 + 27x + 140 - 420 = 0 $$ $$ x^2 + 27x - 280 = 0 $$ 9. **Solve the quadratic equation:** Use the quadratic formula $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$ where $a=1$, $b=27$, and $c=-280$. 10. **Calculate the discriminant:** $$ \Delta = 27^2 - 4 \times 1 \times (-280) = 729 + 1120 = 1849 $$ 11. **Find the roots:** $$ x = \frac{-27 \pm \sqrt{1849}}{2} = \frac{-27 \pm 43}{2} $$ 12. **Evaluate each root:** - $$ x = \frac{-27 + 43}{2} = \frac{16}{2} = 8 $$ - $$ x = \frac{-27 - 43}{2} = \frac{-70}{2} = -35 $$ 13. **Interpret the solution:** Since $x$ represents an increase in length, it must be positive. So, $x = 8$ feet. **Final answer:** Yaritza should increase each dimension by **8 feet** to triple the area.